We present the results of integral field spectroscopy of the gravitational wave (GW) recoiling black hole candidate 3C 186. The goal of the observations is to study the kinematics of the [OIII]5007 narrow emission line region (NLR) of the quasar, and investigate the origin of the velocity offsets originally measured for different UV lines. The results show that i) the spatial structure of the NLR is complex. The [OIII]5007 line shows significant velocity offsets with respect to the systemic redshift of the source. Different components at different velocities (-670, -100, + 75 km s^-1) are produced in different regions of the source. ii) we detect both the narrow and the broad components of the Hbeta line. The narrow component generally follows the kinematics of the [OIII] line, while the broad component is significantly blue-shifted. The peak of the broad line is near the blue end, or possibly outside of the sensitivity band of the instrument, implying a velocity offset of >~1800 km s^-1. This result is in agreement with the interpretation of the QSO as a GW recoiling black hole. The properties of the NLR show that the observed outflows are most likely the effect of radiation pressure on the (photoionized) gas in the interstellar medium of the host galaxy.